Express the equation $\frac{x - 2}{x - 3} + \frac{x - 4}{x - 5} = \frac{10}{3}$; $(x
eq 3, 5)$ as a quadratic equation in standard form. Hence, find the roots of the equation so formed.

Question

Express the equation $\frac{x - 2}{x - 3} + \frac{x - 4}{x - 5} = \frac{10}{3}$; $(x 
eq 3, 5)$ as a quadratic equation in standard form. Hence, find the roots of the equation so formed.

Accepted Answer

Step 1: $\frac{x - 2}{x - 3} + \frac{x - 4}{x - 5} = \frac{10}{3}$
$\Rightarrow \frac{(x - 2)(x - 5) + (x - 4)(x - 3)}{(x - 3)(x - 5)} = \frac{10}{3}$
Step 2: Simplifying, we get $2x^2 - 19x + 42 = 0$
Step 3: $\Rightarrow (x - 6)(2x - 7) = 0$
$\Rightarrow x = 6$ or $x = \frac{7}{2}$

Question

Solution